Log24

Wednesday, May 5, 2010

Symmetry and Parallelisms

Filed under: General,Geometry — m759 @ 10:00 AM

From a post of Peter J. Cameron today —

"… I want to consider the question: What is the role of the symmetric group in mathematics? "

Cameron's examples include, notably, parallelisms of lines in affine spaces over GF(2).

Monday, September 15, 2014

A Seventh Seal

Filed under: General,Geometry — m759 @ 10:00 AM

This post was suggested by the two previous posts, Sermon and Structure.

IMAGE- Epigraph to Ch. 7 of Cameron's 'Parallelisms of Complete Designs'- '...fiddle with pentagrams...' from 'Four Quartets'

Vide  below the final paragraph— in Chapter 7— of Cameron’s Parallelisms ,
as well as Baudelaire in the post Correspondences :

Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….

— Baudelaire, “Correspondances “

A related image search (click to enlarge):

Sunday, September 14, 2014

Sermon

Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

Epigraphs from Parallelisms of Complete Designs
by Peter J. Cameron (Cambridge University Press, 1976)

Introduction
Through the unknown, remembered gate
When the last of earth left to discover
Is that which was the beginning
(T. S. Eliot: Little Gidding)

I  The existence theorem
Here the impossible union
Of spheres of existence is actual
(T. S. Eliot: The Dry Salvages)

II  The parallelogram property
A condition of complete simplicity
(Costing not less than everything)
(T. S. Eliot: Little Gidding)

III  Steiner points and Veblen points
You say I am repeating
Something I have said before. I shall say it again.
Shall I say it again?
(T. S. Eliot: East Coker)

IV  Edge-colourings of complete graphs
And hollyhocks that aim too high
Red into grey and tumble down
(T. S. Eliot: East Coker)

V  Biplanes and metric regularity
Two and two, necessarye conjunction,
Holding eche other by the hand or the arm
Whiche betokeneth concorde.
(T. S. Eliot: East Coker)

VI  Automorphism groups
At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement.
(T. S. Eliot: Burnt Norton)

VII  Resolutions and partition systems
… fiddle with pentagrams
Or barbituric acids, or dissect
The recurrent image into pre-conscious terrors .. .
(T. S. Eliot: The Dry Salvages)

Friday, November 1, 2013

Cameron’s Group Theory Notes

Filed under: General,Geometry — Tags: , — m759 @ 7:00 AM

In "Notes on Finite Group Theory"
by Peter J. Cameron (October 2013),
http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf,
some parts are particularly related to the mathematics of
the 4×4 square (viewable in various ways as four quartets)—

  • Definition 1.3.1, Group actions, and example on partitions of a 4-set, p. 19.
  • Exercise 1.1, The group of Fano-plane symmetries, p. 35.
  • Exercise 2.17, The group of the empty set and the 15 two-subsets of a six-set, p. 66.
  • Section 3.1.2, The holomorph of a group, p. 70.
  • Exercise 3.7, The groups A8 and AGL(4,2), p. 78.

Cameron is the author of Parallelisms of Complete Designs ,
a book notable in part for its chapter epigraphs from T.S. Eliot's
Four Quartets . These epigraphs, if not the text proper, seem
appropriate for All Saints' Day.

But note also Log24 posts tagged Not Theology.

Tuesday, July 9, 2013

Vril Chick

Filed under: General,Geometry — m759 @ 4:30 AM

Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo

Profile picture for "Jo Lyxe" (Josefine Lyche) at Vimeo

Compare to an image of Vril muse Maria Orsitsch.

From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —

Josefine Lyche
Born in 1973 in Bergen, Norway.
Lives and works in Oslo and Berlin.

Keywords (to help place my artwork in the
proper context): Aliens, affine geometry, affine
planes, affine spaces, automorphisms, binary
codes, block designs, classical groups, codes,
coding theory, collineations, combinatorial,
combinatorics, conjugacy classes, the Conwell
correspondence, correlations, Cullinane,
R. T. Curtis, design theory, the diamond theorem,
diamond theory, duads, duality, error correcting
codes, esoteric, exceptional groups,
extraterrestrials, finite fields, finite geometry, finite
groups, finite rings, Galois fields, generalized
quadrangles, generators, geometry, GF(2),
GF(4), the (24,12) Golay code, group actions,
group theory, Hadamard matrices, hypercube,
hyperplanes, hyperspace, incidence structures,
invariance, Karnaugh maps, Kirkman’s schoolgirls
problem, Latin squares, Leech lattice, linear
groups, linear spaces, linear transformations,
Magick, Mathieu groups, matrix theory, Meno,
Miracle Octad Generator, MOG, multiply transitive
groups, occultism, octahedron, the octahedral
group, Orsic, orthogonal arrays, outer automorphisms,
parallelisms, partial geometries,
permutation groups, PG(3,2), Plato, Platonic
solids, polarities, Polya-Burnside theorem, projective
geometry, projective planes, projective
spaces, projectivities, Pythagoras, reincarnation,
Reed-Muller codes, the relativity problem,
reverse engineering, sacred geometry, Singer
cycle, skew lines, Socrates, sporadic simple
groups, Steiner systems, Sylvester, symmetric,
symmetry, symplectic, synthemes, synthematic,
Theosophical Society tesseract, Tessla, transvections,
Venn diagrams, Vril society, Walsh
functions, Witt designs.

(See also the original catalog page.)

Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.

For some background, see (for instance) 
Conspiracy Theories and Secret Societies for Dummies .

Sunday, May 19, 2013

Priority Claim

Filed under: General,Geometry — Tags: , , , — m759 @ 9:00 AM

From an arXiv preprint submitted July 18, 2011,
and last revised on March 11, 2013 (version 4):

"By our construction, this vector space is the dual
of our hypercube F24 built on I \ O9. The vector space
structure of the latter, to our knowledge, is first
mentioned by Curtis
in [Cur89]. Hence altogether
our proposition 2.3.4 gives a novel geometric
meaning in terms of Kummer geometry to the known
vector space structure on I \ O9."

[Cur89] reference:
 R. T. Curtis, "Further elementary techniques using
the miracle octad generator," Proc. Edinburgh
Math. Soc. 
32 (1989), 345-353 (received on
July 20, 1987).

— Anne Taormina and Katrin Wendland,
    "The overarching finite symmetry group of Kummer
      surfaces in the Mathieu group 24 ,"
     arXiv.org > hep-th > arXiv:1107.3834

"First mentioned by Curtis…."

No. I claim that to the best of my knowledge, the 
vector space structure was first mentioned by me,
Steven H. Cullinane, in an AMS abstract submitted
in October 1978, some nine years before the
Curtis article.

Update of the above paragraph on July 6, 2013—

No. The vector space structure was described by
(for instance) Peter J. Cameron in a 1976
Cambridge University Press book —
Parallelisms of Complete Designs .
See the proof of Theorem 3A.13 on pages 59 and 60.

The vector space structure as it occurs in a 4×4 array
of the sort that appears in the Curtis Miracle Octad
Generator may first have been pointed out by me,
Steven H. Cullinane,
 in an AMS abstract submitted in
October 1978, some nine years before the Curtis article.

See Notes on Finite Geometry for some background.

See in particular The Galois Tesseract.

For the relationship of the 1978 abstract to Kummer
geometry, see Rosenhain and Göpel Tetrads in PG(3,2).

Wednesday, December 19, 2012

Identity Shining Forth

Filed under: General,Geometry — Tags: — m759 @ 1:14 PM

From William M. Kantor's 1978 review of Peter J. Cameron's
1976 book Parallelisms of Complete Designs

"There are three ways an area of mathematics
can be surveyed: by a vast, comprehensive treatise;
by a monograph on a small corner of the field; or by
a monograph on a cross section."

An area of mathematics—

A small corner of the field—

A cross section—

Commentary:

The area— Four.
The corner— Identity.
The cross section— Window.

The three ways— December 8  ten years ago.

Thursday, February 16, 2012

Midnight in the Garden

Filed under: General,Geometry — m759 @ 12:00 AM

(Continued from February 10.)

A passage suggested by the T.S. Eliot epigraphs in
Parallelisms of Compete Designs , by a weblog post
of Peter J. Cameron yesterday, and by this journal's
"Within You Without You" posts—

http://www.log24.com/log/pix12/120215-Campbell-InnerOuter.jpg
— Joseph Campbell, The Inner Reaches of Outer Space:
     Metaphor as Myth and as Religion ,
New World Library,
     Second Edition, St. Bridget's Day 2002, page 106

Sunday, January 29, 2012

Declarations

Filed under: General,Geometry — m759 @ 6:00 PM

Weblog posts of two prominent mathematicians today discussed
what appears to be a revolution inspired by the business practices
of some commercial publishers of mathematics.

See Gowers and Cameron.

My own concern is more with the so-called "Non-Euclidean Revolution"
described by Richard Trudeau in a book of that title (Birkhäuser, 1987).

A 1976 document relevant to the concerns in the Trudeau book—

Though not as well known as another document discussing
"self-evident" truths, Cameron's remarks are also of some
philosophical interest.

They apply to finite  geometry, a topic unknown to Euclid,
but nevertheless of considerable significance for the foundations  
of mathematics.

"The hand of the creative artist, laid upon the major premise,
 rocks the foundations of the world." — Dorothy Sayers

Saturday, August 20, 2011

Castle Rock

Filed under: General,Geometry — m759 @ 6:29 PM

Happy birthday to Amy Adams
(actress from Castle Rock, Colorado)

"The metaphor for metamorphosis…" —Endgame

Related material:

"The idea that reality consists of multiple 'levels,' each mirroring all others in some fashion, is a diagnostic feature of premodern cosmologies in general…."

Scholarly paper on "Correlative Cosmologies"

"How many layers are there to human thought? Sometimes in art, just as in people’s conversations, we’re aware of only one at a time. On other occasions, though, we realize just how many layers can be in simultaneous action, and we’re given a sense of both revelation and mystery. When a choreographer responds to music— when one artist reacts in detail to another— the sensation of multilayering can affect us as an insight not just into dance but into the regions of the mind.

The triple bill by the Mark Morris Dance Group at the Rose Theater, presented on Thursday night as part of the Mostly Mozart Festival, moves from simple to complex, and from plain entertainment to an astonishingly beautiful and intricate demonstration of genius….

'Socrates' (2010), which closed the program, is a calm and objective work that has no special dance excitement and whips up no vehement audience reaction. Its beauty, however, is extraordinary. It’s possible to trace in it terms of arithmetic, geometry, dualism, epistemology and ontology, and it acts as a demonstration of art and as a reflection of life, philosophy and death."

— Alastair Macaulay in today's New York Times

SOCRATES: Let us turn off the road a little….

Libretto for Mark Morris's 'Socrates'

See also Amy Adams's new film "On the Road"
in a story from Aug. 5, 2010 as well as a different story,
Eightgate, from that same date:

A 2x4 array of squares

The above reference to "metamorphosis" may be seen,
if one likes, as a reference to the group of all projectivities
and correlations in the finite projective space PG(3,2)—
a group isomorphic to the 40,320 transformations of S8
acting on the above eight-part figure.

See also The Moore Correspondence from last year
on today's date, August 20.

For some background, see a book by Peter J. Cameron,
who has figured in several recent Log24 posts—

http://www.log24.com/log/pix11B/110820-Parallelisms60.jpg

"At the still point, there the dance is."
               — Four Quartets

Friday, August 20, 2010

The Moore Correspondence

Filed under: General,Geometry — m759 @ 5:01 PM

There is a remarkable correspondence between the 35 partitions of an eight-element set H into two four-element sets and the 35 partitions of the affine 4-space L over GF(2) into four parallel four-point planes. Under this correspondence, two of the H-partitions have a common refinement into 2-sets if and only if the same is true of the corresponding L-partitions (Peter J. Cameron, Parallelisms of Complete Designs, Cambridge U. Press, 1976, p. 60). The correspondence underlies the isomorphism* of the group A8 with the projective general linear group PGL(4,2) and plays an important role in the structure of the large Mathieu group M24.

A 1954 paper by W.L. Edge suggests the correspondence should be named after E.H. Moore. Hence the title of this note.

Edge says that

It is natural to ask what, if any, are the 8 objects which undergo
permutation. This question was discussed at length by Moore…**.
But, while there is no thought either of controverting Moore's claim to
have answered it or of disputing his priority, the question is primarily
a geometrical one….

Excerpts from the Edge paper—

http://www.log24.com/log/pix10B/100820-Edge-Geometry-1col.gif

Excerpts from the Moore paper—

Pages 432, 433, 434, and 435, as well as the section mentioned above by Edge— pp. 438 and 439

* J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Oxford U. Press, 1985, p. 72

** Edge cited "E.H. Moore, Math. Annalen, 51 (1899), 417-44." A more complete citation from "The Scientific Work of Eliakim Hastings Moore," by G.A. Bliss,  Bull. Amer. Math. Soc. Volume 40, Number 7 (1934), 501-514— E.H. Moore, "Concerning the General Equations of the Seventh and Eighth Degrees," Annalen, vol. 51 (1899), pp. 417-444.

Sunday, May 2, 2010

Today’s Sermon

Filed under: General — m759 @ 9:29 AM

The Secret Life of Walter Murphy

Continued from last night

"On 1 March 07, I was scheduled
 to fly on American Airlines…."

A tale by the late Walter F. Murphy,
professor emeritus of constitutional law at Princeton

Related material:

A hymn for Murphy — "I'll Fly Away."

See also this journal on
that same date– 1 March 07— along with

Parallelisms of Complete Designs and

Parallelism in Hebrew Poetry.

Tuesday, February 16, 2010

Mysteries of Faith

Filed under: General,Geometry — m759 @ 9:00 AM

From today's NY Times

http://www.log24.com/log/pix10/100216-NYTobits.jpg

Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death–

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death–

2x2x2 cube

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
  and the death of Coxeter–

Putting Descartes Before Dehors

     Binary coordinates for a 4x2 array  Chess knight formed by a Singer 7-cycle

For a more Protestant meditation,
see The Cross of Descartes

Descartes

Descartes's Cross

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Quine and Derrida at Notre Dame Philosophical Reviews

Notre Dame Philosophical Reviews

Friday, February 5, 2010

The Great Brown

Filed under: General,Geometry — m759 @ 9:00 PM

Today's New York Times on a current theatrical presentation of The Great Gatsby

"Throughout the show, the relationship between what is read and its context keeps shifting, with the real world finally giving way entirely to the fictive one."

Owl Eyes in The Great Gatsby

"This fella's a regular Belasco."

http://www.log24.com/log/pix10/100204-DavidBrownSm.jpg

David Brown, producer. Brown died on Monday.

From The Diamond as Big as the Monster in this journal on Dec. 21, 2005–

"At the still point, there the dance is.” –T. S. Eliot, Four Quartets

Eliot was quoted in the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron, published when Cameron was at Merton College, Oxford.

“As Gatsby closed the door of ‘the Merton College Library’ I could have sworn I heard the owl-eyed man break into ghostly laughter.” –F. Scott Fitzgerald

Related material: Yesterday's posts and the jewel in Venn's lotus.

Friday, December 4, 2009

Parallelism

Filed under: General,Geometry — m759 @ 12:00 AM

From Peter J. Cameron's
Parallelisms of Complete Designs (pdf)–

Epigraph by Eliot on Little Gidding in Cameron's 'Parallelisms'

"…the Feast of Nicholas Ferrar
  is kept on the 4th December."

Little Gidding Church

Cameron's is the usual definition
of the term "non-Euclidean."
I prefer a more logical definition.

Tuesday, November 10, 2009

Out of Inland

Filed under: General,Geometry — m759 @ 11:02 AM

Epigraphs at
Peter Cameron’s home page:

Quotes from 'The Hawkline Monster' and 'Riddley Walker'

See also the epigraphs in Cameron’s
Parallelisms of Complete Designs,
entries on this date three years ago,
Russell Hoban in this journal,
and
The Hawkline Monster in this journal.

Wednesday, November 19, 2008

Wednesday November 19, 2008

Filed under: General,Geometry — Tags: , — m759 @ 5:01 PM

"Through the unknown,
remembered gate…."

Four Quartets

(Epigraph to the introduction,
Parallelisms of Complete Designs
by Peter J. Cameron,
Merton College, Oxford)

"It's still the same old story…."
— Song lyric

The Great Gatsby
Chapter 6:

"An instinct toward his future glory had led him, some months before, to the small Lutheran college of St. Olaf in southern Minnesota. He stayed there two weeks, dismayed at its ferocious indifference to the drums of his destiny, to destiny itself, and despising the janitor’s work with which he was to pay his way through."

There is a link to an article on St. Olaf College in Arts & Letters Daily  today:

"John Milton, boring? Paradise Lost  has a little bit of something for everybody. Hot sex! Hellfire! Some damned good poetry, too…" more»

The "more" link is to The Chronicle of Higher Education.

For related material on Paradise Lost  and higher education, see Mathematics and Narrative.

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
 
ART WARS:
To Apollo
 
The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
(10/09/02)
Balanchine's Birthday
(01/09/03)

Art Theory for Yom Kippur
(10/05/03)

A Form
(05/22/04)
Ineluctable
(05/27/04)

A Form, continued
(06/05/04)
Parallelisms
(06/06/04)
Ado
(06/25/04)

Deep Game
(06/26/04)
Gameplayers of Zen
(06/27/04)
And So To Bed
(06/29/04)
Translation Plane for Rosh Hashanah
(09/15/04)
Derrida Dead
(10/09/04)
The Nine
(11/09/04)
From Tate to Plato
(11/19/04)
Art History
(05/11/05)
A Miniature Rosetta Stone
(08/06/05)
High Concept
(8/23/05) 
High Concept, Continued
(8/24/05)
Analogical Train of Thought
(8/25/05)
Today's Sermon: Magical Thinking
(10/09/05)
Balance
(10/31/05)
Matrix
(11/01/05)
Seven is Heaven, Eight is a Gate
(11/12/05)
Nine is a Vine
(11/12/05)
Apollo and Christ
(12/02/05)
Hamilton's Whirligig
(01/05/06)
Cross
(01/06/06)
On Beauty
(01/26/06)
Sunday Morning
(01/29/06)
Centre
(01/29/06)
New Haven
(01/29/06) 
Washington Ballet
(02/05/06)
Catholic Schools Sermon
(02/05/06)
The Logic of Apollo
(02/05/06)
Game Boy
(08/06/06)
Art Wars Continued: The Krauss Cross
(09/13/06)
Art Wars Continued: Pandora's Box
(09/16/06)
The Pope in Plato's Cave
(09/16/06)
Today's Birthdays
(09/26/06)
Symbology 101
(09/26/06)

Tuesday, October 3, 2006

Tuesday October 3, 2006

Filed under: General,Geometry — m759 @ 9:26 AM

Serious

"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."

Charles Matthews at Wikipedia, Oct. 2, 2006

"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

— G. H. Hardy, A Mathematician's Apology

Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:

Affine group‎
Reflection group‎
Symmetry in mathematics‎
Incidence structure‎
Invariant (mathematics)‎
Symmetry‎
Finite geometry‎
Group action‎
History of geometry‎

This would appear to be a fairly large complex of mathematical ideas.

See also the following "large complex" cited, following the above words of Hardy, in Diamond Theory:

Affine geometry, affine planes, affine spaces, automorphisms, binary codes, block designs, classical groups, codes, coding theory, collineations, combinatorial, combinatorics, conjugacy classes, the Conwell correspondence, correlations, design theory, duads, duality, error correcting codes, exceptional groups, finite fields, finite geometry, finite groups, finite rings, Galois fields, generalized quadrangles, generators, geometry, GF(2), GF(4), the (24,12) Golay code, group actions, group theory, Hadamard matrices, hypercube, hyperplanes, hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman's schoolgirl problem, Latin squares, Leech lattice, linear groups, linear spaces, linear transformations, Mathieu groups, matrix theory, Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads, the octahedral group, orthogonal arrays, outer automorphisms, parallelisms, partial geometries, permutation groups, PG(3,2), polarities, Polya-Burnside theorem, projective geometry, projective planes, projective spaces, projectivities, Reed-Muller codes, the relativity problem, Singer cycle, skew lines,  sporadic simple groups, Steiner systems, symmetric, symmetry, symplectic, synthemes, synthematic, tesseract, transvections, Walsh functions, Witt designs.

Friday, April 28, 2006

Friday April 28, 2006

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Exercise

Review the concepts of integritas, consonantia,  and claritas in Aquinas:

"For in respect to beauty three things are essential: first of all, integrity or completeness, since beings deprived of wholeness are on this score ugly; and [secondly] a certain required design, or patterned structure; and finally a certain splendor, inasmuch as things are called beautiful which have a certain 'blaze of being' about them…."

Summa Theologiae Sancti Thomae Aquinatis, I, q. 39, a. 8, as translated by William T. Noon, S.J., in Joyce and Aquinas, Yale University Press, 1957

Review the following three publications cited in a note of April 28, 1985 (21 years ago today):

(1) Cameron, P. J.,
     Parallelisms of Complete Designs,
     Cambridge University Press, 1976.

(2) Conwell, G. M.,
     The 3-space PG(3,2) and its group,
     Ann. of Math. 11 (1910) 60-76.

(3) Curtis, R. T.,
     A new combinatorial approach to M24,
     Math. Proc. Camb. Phil. Soc.
    
79 (1976) 25-42.

Discuss how the sextet parallelism in (1) illustrates integritas, how the Conwell correspondence in (2) illustrates consonantia, and how the Miracle Octad Generator in (3) illustrates claritas.
 

Wednesday, December 21, 2005

Wednesday December 21, 2005

Filed under: General,Geometry — m759 @ 4:07 PM
For the feast of
St. Francis Scott Key Fitzgerald

The Diamond
as Big as
the Monster

From Fitzgerald’s The Diamond as Big as the Ritz:

    “Now,” said John eagerly, “turn out your pocket and let’s see what jewels you brought along. If you made a good selection we three ought to live comfortably all the rest of our lives.”
     Obediently Kismine put her hand in her pocket and tossed two handfuls of glittering stones before him.
    “Not so bad,” cried John, enthusiastically. “They aren’t very big, but– Hello!” His expression changed as he held one of them up to the declining sun. “Why, these aren’t diamonds! There’s something the matter!”
    “By golly!” exclaimed Kismine, with a startled look. “What an idiot I am!”
    “Why, these are rhinestones!” cried John.

From The Hawkline Monster, by Richard Brautigan:
 
    “What are we going to do now?” Susan Hawkline said, surveying the lake that had once been their house.
    Cameron counted the diamonds in his hand.  There were thirty-five diamonds and they were all that was left of the Hawkline Monster.
    “We’ll think of something,” Cameron said.

Related material:

“A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces.”

When Novelists Become Cubists:
    The Prose Ideograms of Guy Davenport,
    by Andre Furlani

“T.S. Eliot’s experiments in ideogrammatic method are equally germane to Davenport, who shares with the poet an avant-garde aesthetic and a conservative temperament.  Davenport’s text reverberates with echoes of Four Quartets.”

Andre Furlani

“At the still point,
  there the dance is.”

—  T. S. Eliot, Four Quartets,
quoted in the epigraph to
the chapter on automorphism groups
in Parallelisms of Complete Designs,
by Peter J. Cameron,
published when Cameron was at
Merton College, Oxford.

“As Gatsby closed the door of
‘the Merton College Library’
I could have sworn I heard
the owl-eyed man
break into ghostly laughter.”

F. Scott Fitzgerald

Friday, January 7, 2005

Friday January 7, 2005

Filed under: General,Geometry — m759 @ 7:59 AM

In Memory of
Guy Davenport

From the day Davenport died:

The image “http://www.log24.com/log/pix05/050104-Endgame.jpg” cannot be displayed, because it contains errors.

“At Merton College, Oxford,
he wrote the first thesis on Joyce
to be accepted by the university.”

Today’s New York Times

From a very informative essay
on Davenport’s aesthetics:

“T.S. Eliot’s experiments
in ideogrammatic method
are equally germane to Davenport,
who shares with the poet
an avant-garde aesthetic and
a conservative temperament.
Davenport’s text reverberates
with echoes of Four Quartets.”

— Andre Furlani

“At the still point, there the dance is.”

—  T. S. Eliot, Four Quartets,
quoted in the epigraph to
the chapter on automorphism groups
in Parallelisms of Complete Designs,
by Peter J. Cameron,
published when Cameron was at
Merton College, Oxford.

See also
Elegance.

Tuesday, June 29, 2004

Tuesday June 29, 2004

Filed under: General,Geometry — m759 @ 2:22 PM
And So To Bed

Advanced Study (6/26/04), continued…

Part I: Ulysses

When?

Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.

Where?

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Ulysses, conclusion of Ch. 17

Part II: Badcoc

A Visual Meditation for
the Feast of St. Peter

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For further details on this structure, see

Magic Squares, Finite Planes,
and Points of Inflection
on Elliptic Curves
,
by Ezra Brown, and

Visualizing GL(2, p)
by Steven H. Cullinane.

For a more literary approach
to this structure, see

Balanchine’s Birthday (Jan. 9, 2003),
Art Theory for Yom Kippur (Oct. 5, 2003),
A Form (May 22, 2004),
Ineluctable (May 27, 2004),
A Form, continued (June 5, 2004),
Parallelisms (June 6, 2004),
Deep Game (June 26, 2004), and
Gameplayers of Zen (June 27, 2004).

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To appreciate fully this last entry
on Gameplayers,
one must understand
the concept of “suicide”
in the game of Go

and be reminded
by the fatuous phrase of the
Institute of Contemporary Art
quoted in Gameplayers
encompassed by ‘nothing’ ” —
of John 1:5.

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Sunday, June 6, 2004

Sunday June 6, 2004

Filed under: General,Geometry — m759 @ 1:28 PM
Parallelisms

“I confess I do not believe in time.
I like to fold my magic carpet,
after use, in such a way
as to superimpose
one part of the pattern
upon another.”

(Nabokov, Speak, Memory)

From a review of On the Composition of Images, Signs & Ideas, by Giordano Bruno:

Proteus in the House of Mnemosyne (which is the fifth chapter of the Third Book) relies entirely on familiarity with Vergil’s Aeneid (even when the text shifts from verse to prose). The statement, “Proteus is, absolutely, that one and the same subject matter which is transformable into all images and resemblances, by means of which we can immediately and continually constitute order, resume and explain everything,” reads less clear than the immediate analogy, “Just as from one and the same wax we awaken all shapes and images of sensate things, which become thereafter the signs of all things that are intelligible.”

From an interview with Vladimir Nabokov published in Wisconsin Studies in Contemporary Literature, vol. VIII, no. 2, Spring 1967:

When I was your student, you never mentioned the  Homeric parallels in discussing Joyce’s Ulysses  But you did supply “special information” in introducing many of the masterpieces: a map of Dublin for Ulysses….  Would you be able to suggest some equivalent for your own readers?

Joyce himself very soon realized with dismay that the harping on those essentially easy and vulgar “Homeric parallelisms” would only distract one’s attention from the real beauty of his book. He soon dropped these pretentious chapter titles which already were “explaining” the book to non-readers.  In my lectures I tried to give factual data only. A map of three country estates with a winding river and a figure of the butterfly Parnassius mnemosyne for a cartographic cherub will be the endpaper in my revised edition of Speak, Memory.

For more on Joyce and Proteus,
see the May 27 entry
Ineluctable.

Saturday, April 19, 2003

Saturday April 19, 2003

Filed under: General — m759 @ 2:56 PM

Claves Regni Caelorum

“June dawns, July noons, August evenings over, finished, done, and gone forever with only the sense of it all left here in his head. Now, a whole autumn, a white winter, a cool and greening spring to figure sums and totals of summer past. And if he should forget, the dandelion wine stood in the cellar, numbered huge for each and every day. He would go there often, stare straight into the sun until he could stare no more, then close his eyes and consider the burned spots, the fleeting scars left dancing on his warm eyelids; arranging, rearranging each fire and reflection until the pattern was clear.”
— Ray Bradbury, Dandelion Wine

“Socialism or Death”
— Banner in the film “Guantanamera” (Cuba, 1994)

“I’m thinking, I’m thinking!”
Jack Benny, replying to bandits who demanded his money or his life.  Benny was born on St. Valentine’s day and died on St. Stephen’s day.

For what it’s worth, both Bradbury and Benny are from Waukegan, Illinois.

“Through the unknown, remembered gate….”
— T. S. Eliot, epigraph to
Parallelisms of Complete Designs, by

Peter J. Cameron

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